Barometric Distribution of Hard Sphere Gas

Gas particle distribution simulated by hard spheres and located in a gravitational field at a constant temperature is under study. A hard sphere model is poorly applicable to real gases, but it can be used to describe the distribution of nanoparticles in a colloidal suspension. Various models of weakly nonideal gas are compared: virial expansion up to a second coefficient, a Wertheim-Thiel equation in a Percus-Yevick approximation, and a Carnahan-Starling approximation. In the case of virial expansion, an exact analytical solution for an equation of particle distribution by height is obtained. For more complex models, solutions are found using numerical methods. It is shown that accounting for a finite particle size leads to significant changes in the particle distribution as compared to the ideal gas distribution even at small volume fractions. The results obtained using virial expansion are in good agreement with the results obtained using more complex models provided that the volume fraction of the impurity does not exceed 0.1.